The theory of Gamma-semigroups is an extension of the semigroup theory. In this paper, we have studied some new results on right multiplication Gamma-semigroups. Particularly, the condition for a principal right ideal Gamma-semigroup to be a right multiplication Gamma-semigroup and the construction of larger right multiplication Gamma-semigroups by considering the direct product.
In this paper, we study a differential equation of fractional order in which the nonlinear term depends on the Riemann-Liouville integral of an unknown function. By using both Banach contraction mapping and Schaefer fixed point theorem, an existence and uniqueness result is obtained. We close this work with an illustrative example.
In this paper, we use the k-weighted fractional integral of functions with respect to another function to generalize Tchebyshev-type fractional integral inequalities. Some inequalities involving k-weighted fractional integrals are also be proved.
Using the decomposition of the Nehari manifold, we study the multiplicity of positive solutions for a certain elliptic problem.
The idea proposed in this work is to investigate the decay estimate of the energy to the $p$-Laplacian wave equation with a weak nonlinear dissipation and source term. The proof is based on the multiplier techniques combined with nonlinear integral inequalities given by Martinez.
n this work, we study the commutativity of 3-prime near-rings admitting homoderivations that satisfy certain conditions. Additionally, we offer a counter example to demonstrate that the assumption of 3-primeness in our theorems is crucial.
In this paper, we investigate the countable tightness, the countable strong fan tightness, the countable fan tightness, the strictly Frechet-Urysohn property and the selectively strictly A-property of the function space of all continuous functions from a metric space X, endowed with the Cauchy convergence topology, to the real line R.
Given a normed space (X,||.||) and a linear (unbounded and not densely defined) operator A, defined on a subset D of X and with values in X, we show how to define norms |||.||| on X such that the operator A (viewed as an operator from D, endowed with the norm ||.||, with values in X, endowed with the norm |||.|||)) becomes bounded and D becomes dense with respect to |||.|||. We then apply our results to m-accretive operators.
In this paper, we introduce the notion of vector valued weak affine bi-frames in reducing subspaces of L^2(R_+, C^L) and obtain a characterization of these frames by using Walsh-Fourier transform.
Let L be a bounded distributive lattice. The join-essential element graph JE(L) of L is a graph whose vertices are all nontrivial elements (i.e. different from 1 and 0) of L and two distinct elements x and y are adjacent if and only if x v y is an essential element of L. The basic properties and possible structures of the graph JE(L) and its subgraph PE(L) induced by vertices which are not essential as elements of L are investigated.
Based on the topological degree method for a class of bounded and demicontinuous operators of type S_+ and properties of variable exponent Sobolev spaces, we study the existence of weak solutions for a nonlinear Dirichlet problem of capillary phenomena involving an equation driven by the p(x)-Laplacian-like operator.
In this paper, we introduce and study a new second order resolvent dynamical system associated with a class of mixed general variational inequalities. We suggest some new multi-step iterative methods for solving the mixed variational inequalities using the forward finite difference schemes. These methods include Mann, Ishikawa and Noor iterations as special cases.
A new inertial extragradient algorithm for approximating solutions of some class of split variational inequality problem in real Hilbert space is introduced and discussed. Furthermore, the sequence generated by our algorithm is shown to converge strongly to the solution of the aforementioned problem. Our result is obtained without the assumption of the Lipschitz constant of the underline operator, and also with minimal number of projections per iteration compare to other results on split variational inequality problems in the literature. A numerical example is presented to demonstrate and compare the versatility of our result. Our result extends and improves many recent results of this type in the literature.
The aim of this paper is to consider the nonlinear Korteweg-de Vries equation with internal feedback without delay and a boundary feedback with time-dependent delay. We study the well-posedness of the system under some assumptions on the length of the spatial domain and on the delay using semigroups theory and we study the exponential stability of the equation considering a Lyapunov functional approach.
Recently, Abbas has introduced and investigated the notion of h-open sets. In this paper, to generalize h-open sets, we introduce hI-open sets in an ideal topological space, and we obtain some properties of hI-open sets. We also introduce and investigate hI-continuous functions in an ideal topological space.
In this paper, we define a particular class of h-admissible Fourier integral operators F_h. These classes of Integral operators turn out to be bounded on the Schwartz space and on its dual. Moreover, we show that F_h can be extended as a Hilbert-Schmidt operators on L^2(R^n).
In this paper, we will discuss the fixed point theory of triangular operators in the setting of generalized metric spaces and for contraction type operators. Global asymptotic stability of the fixed point, well-posedness of the fixed point problem, Ulam-Hyers stability and Ostrowski property are investigated. Some applications of the basic fibre contraction principles are also considered.
In this paper, we define a generalized notion of semidirect hyperproduct of polygroups and use that to introduce a pushout construction for crossed polymodules. Our results extend the classical results of crossed squares to crossed polysquares. One of the main tools in the study to polygroups is the fundamental relations. Additionally we study of the crossed polysquare version of homotopy cokernels.
The main objective of this paper is to study a weak solution for a certain parabolic problem, defined on an open subset of R^n with smooth boundary. By using the Galerkin approximation and a family of potential wells, we obtain the existence of a global solution and finite time blow-up under some suitable conditions. On the other hand, the results for asymptotic behavior for certain solution with positive initial energy are also given.
In this note, we introduce a new degree-based descriptive parameter, namely, the degree polynomial-pair (DPP), for the edges of a simple graph. This notion leads to a concept, namely, the degree polynomial-pair sequence (DPPS) in graphs. We show that the DPPS of a graph gives more information about the graph than its degree polynomial sequence does, but it still does not identify the graph uniquely. We obtain the DPPS for some well-known graphs. Also we prove a theorem in which a necessary condition for the graphic realizability of a sequence of polynomial pairs is given. Several open problems concerning these subjects are given as well.
